Asalamo Alaikum I heard that Dhikr by pronouncing only the name of "Allah" is not permissible. So is it permissible?
There seems to be a difference of opinion on the matter. SeekersHub (Hanafi, Sunni) considered it a permissible form of dhikr:
The Divine Command to ‘make much remembrance of Allah’ is general, and anything considered ‘remembrance’ (dhikr) fulfills it. Given this, it is permitted by general agreement of the majority of Sunni scholarship to make dhikr of individual names of Allah, such as the Supreme Name, ‘Allah.’
It looks like this refers to Qur'an 33:41: O you who have believed, remember Allah with much remembrance.
However, Islam Q&A (Salafi, which is considered Hanbali, Sunni) have three fatawa on the topic (9389, 26867, and 91305) and they strongly prohibit it. They describe this as a form of innovation, which presumably implies a bad kind of innovation, describing it as:
... invented by the ignorant Sufis and those who follow them.
Islam Q&A fatwa 91305
They mention a difference of opinion in fatwa 9389, but don't take it too seriously.
Fatwa 91305 mentions a hadith, which I think is the following (or something equivalent):
Anas narrated that the Messenger of Allah(s.a.w) said: "The Hour will not be established until 'Allah, Allah is not said on the earth."
Jami` at-Tirmidhi 2207 [grade: sahih]
But they contest it: (a) saying there's other versions with "‘Laa ilaaha ill-Allaah" instead of "Allaah Allaah", (b) arguing how it's illogical, (c) "the name of Allaah on its own does not carry a complete meaning", (d) the companions of the prophet did not have this understanding, and (e) scholarly comments on this hadith do not understand it as referring to dhikr.
Saying "Allah" alone in Dhikr is biddah (innovation); as such, it is not permissible. Here is a good explanation on ruling behind that.